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A method for reparameterizing mild solutions to nonlinear evolution equations. (English) Zbl 0694.35081
Existence of solutions of evolution differential equation \(u'(t)+A(t)u(t)\ni 0\), \(u(0)=x_ 0\) where \(A(t)\) is a multivalued m- accretive operator in a Banach space \(X\) is discussed in the case when a solution to \(v'(t)+B(t)v(t)\ni 0\), \(v(0)=x_ 0\) is known to exist and \(A\) and \(B\) are related by \(A(t)=r(t)B(t)\) with \(r(t)\) positive and integrable.
Reviewer: S.Tersian
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
34G99 Differential equations in abstract spaces
35K55 Nonlinear parabolic equations
Full Text: DOI
[1] Crandall, M.G; Evans, L.C, On the relation of the operator \(∂∂s + ∂∂τ\) to evolution governed by accretive operators, Israel J. math., 21, 261-278, (1975) · Zbl 0351.34037
[2] Crandall, M.G; Pazy, A, Nonlinear evolution equations in Banach spaces, Israel J. math., 11, 57-94, (1972) · Zbl 0249.34049
[3] Craven, B, Lebesgue measure and integral, (1982), Pitman MA · Zbl 0491.28001
[4] Evans, L.C, Nonlinear evolution equations in an arbitrary Banach space, Israel J. math., 26, 1-42, (1977) · Zbl 0349.34043
[5] \scM. A. Freedman, Further investigation of the relation of the operator \(∂∂σ + ∂∂τ\) to evolution governed by accretive operators, Houston J. Math., to appear. · Zbl 0811.35172
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